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All integers n ≥ (a − 1)(b − 1) can be written as n=ua+vb

Source: IMO LongList 1979 - P24

June 1, 2011
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Problem Statement

Let aa and bb be coprime integers, greater than or equal to 11. Prove that all integers nn greater than or equal to (a−1)(b−1)(a - 1)(b - 1) can be written in the form: n=ua+vb,with(u,v)∈N×N.n = ua + vb, \qquad \text{with} (u, v) \in \mathbb N \times \mathbb N.
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